Maybe you found this blog while searching for texts related to physics, maths and/or one of the scientists named Bernoulli. Though, every now and then, I might write about maths, the main scope concerns the world of chess problems - views, experiences, pleasures, moments of frustration (indeed!). In most cases, posts are about solving, constructing, enjoying chess compositions.

31 January 2011

Once again, I introduce a chess variant just requiring the knowledge of the basic rules of chess. Here is an example of how the puzzles look like:

Place the given pieces on the marked squares.
Each number tells how often this square is threatened by a piece.

It's your task to deduce the correct position from the given hints. As you might have guessed already, there is no restriction as to the board size or the amount and types of pieces to be placed. Some web sites deal with this type of puzzle. And there is also software that generates them (though quite old):

28 January 2011

Many Grandmasters composed chess problems, often those were endgame studies. You might think of Pal Benko, Jan Timman or John Nunn. But I was astonished to learn that also the Polgar sisters, Alexei Shirov and Alexander Morozevich have composed, though not as much as the first three I mentioned. Maybe, you like the following study by GM Salov, too.

25 January 2011

Today's subject is Reflex Chess. It was invented in the 1880's by William Geary and B. J. Laws, and was reviewed in the May 1907 issue of Chess Amateur. Orthodox chess rules apply, except that the winner is the player whose king is checkmated. If a move gives mate, then the player must make such a move. It has been used primarily as a problem theme called reflexmate.

Fadil Abdurahmanovic

Bilten 11/1961

r#4

(4+2)

Solution:

White intends to block c2 and get checkmated via e1=Q#. The first step is to control a2, so that Black has to move the pawn.

22 January 2011

As I just wrote about the look back ... there is a sub-genre of chess problems called retros. There, the retrograde analysis plays an important role. It is a technique to determine which moves were played leading to a given position. For instance, you may have to find out exact moves or move orders. In other cases, you must prove a certain move had (not) been played in the course of the (virtual) game.

Here are two examples by the retro specialist Dr. Karl Fabel. I think they are not too difficult but still suitable for demonstration purposes. By the way, there is a project "Ulti-Mate Fabel" with the aim to publish his complete opus. Maybe, it will be finished this year. Watch out for this book!

1

Dr. Karl Fabel

Basler Nachrichten 1964

#1

(11+13)

2

Dr. Karl Fabel

problem 08/1952

#1 (RV)

(10+4)

Now, let's have a look at the diagrams. A mate in 1 move? Solved in a second! Really?

The solution to diagram 1 is 1. Kf2#. Or is it 1. 0-0#? Are there even two solutions? To find out, we must look for hints.

For example, we see that the three white pawns on e3, f3 and g3 captured the three missing black pieces. We can't determine the details, but evidently, e3 came from f2, f3 from g2 and g3 from h2. Also, only a rook could be captured on f3. as the bishop from f8 moves on black squares.

Then we have the Na8. First the knight moved to a8, then there was the capture a7xb6. This means, none of the black rooks could leave the 8th rank via the a-file. Either, there was the pawn on a7 or the knight on a8. Now, that we know this, we further conclude that f7-f5 had to be played before the capture on f3. The captured rooks could only get out via f6! Furthermore, g7-g6 had to be played prior to the capture: either to enable Rh8-g8-g7-f7-f6 etc. or to let the bB leave f8, so that Rh8-f8-f6 etc. was possible.

So, we know that the pawns already were on f5 and g6 when g2xRf3 was played. Now, we arrived at the crucial point. How did the bishops reach their respective squares in the diagram? Obviously, the bB stood on h3 when g2xRf3 happened, this was the only square. After the capture, he blocked the path of the wB. Thus, he had to move to h1, in order to let the wB get to h5. This was the only square to make way.

Wow! We just proved that the wR already had left h1 and later returned. Therefore, White can't castle anymore. Only 1. Kf2# solves the first problem.

How does it feel to be a chess detective? Come on, it is just great! Oh, there was a second diagram. We will crack this puzzle, as well. It also asks to mate in 1 move, but there is something added. "RV" stands for "retro variants". This means, that a certain position does not simply consist of the pieces on their squares but also includes the possible moves (especially castling and e.p. captures) and the history of the position. In such problems, the history of a position cannot be determined with certainty, but each of the alternative histories demands a different solution.

OK, we already know we have to examine Black's last move(s) and must figure out whether White can castle or capture the pawn dxe6 e.p. Both moves deliver the desired mate (and only those).

It is impossible to determine what move Black played last, but clearly it must have been either e7-e5 or something else (law of excluded middle, tertium non datur). So, the solution has two lines.

Let's assume, Black just played e7-e5. Then, bBh4 is a promoted piece, coming from e1 or g1. Therefore, the wK had to move. Promotion on e1 is the trivial case. If Black promoted on g1, then the bishop must have moved to f2 giving check and forcing the wK to leave e1. We see, castling is not allowed. But 1. dxe6 e.p.# solves, as we can prove (we explicitely assumed it) that the last move was e7-e5.

What, if Black did not play e7-e5, maybe just e6-e5 or moved the king or the bishop? Then, the bBh4 can be the original piece and 1. 0-0-0# solves, as we cannot prove that castling is not possible.

19 January 2011

Do you know that? You read or hear a certain word and immediately a picture, a thought or an experience pops up in your mind. If you tell others about it, they might stare at you, wondering what goes on. Or, there is someone just like you, maybe even having similar ideas. Somehow, I have the feeling the general ability (willingness?) to create such an association of ideas decreases due to media overkill, to name just one reason. But I wander from the subject.

Each time I read "strand" or related words, I am reminded of the song Stranded by Manfred Mann's Earth Band. And exactly this happened, as well, when I saw the following diagram. It's another chess puzzle where you just need to know how the pieces move.

T. R. Dawson

Strand Magazine, October 1911

Each White piece captures an unmoved identical adversary,
with no route intersecting any other.

Solution
Starting with the paths of the bishops, it is not that difficult as it might look at first glance. After that, there is not much left for the other pieces:
Bh1-g2-f1-d3-c2-b3-c4-b5-c6-d5-e6-f5-h7-g8-f7-e8-d7-c8-b7xa8.
Be1-d2-c1-a3-b4-a5-c7-d6-e7-f6xg7.
Rh2xh4.
Qc3-d4-f2-g3-g4-h5xh6.
Nf3-g5-e4xc5.

16 January 2011

In the 1980s, I had a lot of mail correspondence (yes, letters sent via mailing delivered by the letter carrier!) with Dr. Werner Speckmann. He was my first contact in the world of chess problems, patiently answering my letters. More than once, he advised me to be more careful whith checking my compositions before sending them to him. Not so easy for a young boy of 16, without any further equipment except a few books.

Anyway, when he saw my interest in fairy chess, he turned my attention to a book which was just published at that time. It was the German translation of A Guide to Fairy Chess by A. S. M. Dickins. Not much later, I bought it and though I didn't understand everything, I learnt quite a lot. Some explanations of pieces, conditions or stipulations in the book are simply not comprehensive enough to get the picture, the more if you are quite new to all this. Very much later, thanks to the Internet, I finally found out more about this and that. I even had the opportunity to have a look at the original version of the book — but I must say it looks even more confusing than the German!

I found a nice miniature composed by Dickins. You'll find the solution without help, right? Just move the bishop ... ?? Yes and no!

13 January 2011

Today some more about the fact that having composed a nice chess problem is not always sufficient — you have to be lucky that nobody else had the same idea before and beat you to it.

Diagram B was shown together with the solution to my composition (diagram A) and obviously it was published before. It was awarded with a first prize, though having a promoted piece and two black pawns which don't do much, especially not in the final position. On the other hand, the solution is less obvious. Anyway, it's too bad I sent in my work "too late" and to the "wrong" magazine.

A

Gerson Berlinger

Europa-Rochade 4/1989

ser-h#31

(14+1)

B

Per Grevlund

Thema Danicum 1990

1st Prize

ser-h#31

(15+3)

You will figure out the solutions on your own, right? Just let the black king visit all four corners and return home to get mated. Clicking on the respective diagram will give you more information.

The second example is the first case I know of where I was quicker. Both problems have the same solution. Do you manage to crack the puzzle? Choose the one you like better.

Gerson Berlinger

Europa-Rochade 3/1987

#6

(9+5)

Michael Barth

Leipziger Volkszeitung, 2010

#6

(8+6)

Finally, there is a really frustrating experience. Last year, in summer, I started to experiment with proof games. Nothing spectacular, just trying out things. But I created some interesting little puzzles. And one of them was actually a real good one, as it combined several themes and apparently nobody else had done this before. So, I sent my composition to a chess problem magazine. Only three weeks later, I learned the bitter truth, browsing through the latest problems having been added to the Chess Problem Database Server. Just a few months earlier, "my" problem had already been published (see diagram). Argh!

10 January 2011

One of the most often reproduced helpmates ever is shown in the following diagram. Five different pieces on a6 lead to five different model mates. Moreover, the composer achieved this with just five pieces. Outstanding!

Henry Forsberg

Revista Romana de Sah 1935

h#2

(3+2)

a) Diagram

b) bRa6

c) bBa6

d) bNa6

e) bPa6

Such a twinning by replacing a piece by any other piece on the same square is no trivial task, especially if you want to have a classic Forsberg twin with all five orthodox pieces. Here are three more problems, the last one featuring some grasshoppers.

07 January 2011

In December, I came across a forum post which mentions an interesting video with a chess/maths puzzle:

A lot of people have tried to come up with a solution. But I think they made several mistakes, as there are more deviations for both Black and White than they have considered. Towards the end of the video, at 7:21, there is a statement (last updated on November 11, 2010) that nobody has solved the puzzle so far. Wrong since December 27, 2010! I did figure out the solution, believe it or not.

In order to determine the correct answer, it's quite helpful to be a problemist (to "see" the different possibilities) and a math enthusiast (to develop a strategy to master the complexity) and also a programmer (machines do the calculation precise and way faster, so why bother with that).

Update January 20, 2011:
In the meantime, the video has been changed. Towards the end, the correct number is given. It looks like the author read this post, as he refers to those things I mentioned in the last paragraph.
The problem in the video was composed by John Nunn. You can read more about it here.

04 January 2011

I guess I managed to find all solutions in both of the solving contests I wrote about in December.

The one in the Stuttgarter Zeitung was tricky as always, but the more often you attempt to solve such types of puzzles, the better you become. But it's always and easily possible that you miss something. Therefore, I won't cheer too early.

Generally speaking, some of the ChessBase puzzles seemed to be quite hard. I didn't mind, for in most cases, I quickly discovered the ideas behind. The autographs were not too difficult to identify, but I am clueless with this astronomy stuff, at least with regards to the third object. All in all, this was a strange contest. After several years without any prizes to win at all, there is the possibility again — with the toughest contest ever and just four (...) prizes. Either you're a problemist to solve the chess puzzles, then you'd rather prefer the book as a prize, if at all. On the other hand, as a chess player collecting autographs, you might like to win the signed software, but it's quite likely that you'll struggle to get there. Hopefully, there'll be some statistics about the number of participants and how many solved what. That'd be really interesting.

As for the Christmas puzzles on Susan Polgar's blog ... yes, I liked (most of) them, too. The proof games were fun, though the third was published with a wrong diagram as you already know. Moreover, it took them a long time to make an attempt to correct it. Why didn't they just give the correct diagram?! Then the Christmas trees. I reckon only the first was actually composed by Pal Benko, as there was no author mentioned for No. 2 and No. 3. Benko's tree had a nice sacrificial key and was the best by far. But the following three-mover was ugly and I am not talking about the colors of the squares. The key, the variations and the duals — no thanks! And the worst was still to come the very next day. This time, a four-mover with three solutions (huh?) and even more duals. A chess player might be happy to just find one of those solutions, not caring that this is supposed to be a chess problem (isn't it?), treating it as any other tactical combination in a game. On the other hand, the problemist gets stomachache. At least, one solution is unique.